2018-05-25T00:09:27Zhttp://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=8802012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1Note on Properties of First Zagreb Index of GraphsM.TAVAKOLIF.RAHBARNIALet G be a graph. The first Zagreb M1(G) of graph G is defined as: M1(G) = uV(G) deg(u)2. In this paper, we prove that each even number except 4 and 8 is a first Zagreb index of a caterpillar. Also, we show that the fist Zagreb index cannot be an odd number. Moreover, we obtain the fist Zagreb index of some graph operations.Topological indicesThe first and second Zagreb indicesTreeGraph operationStrongly distance-balanced graph2012120115http://ijmc.kashanu.ac.ir/article_5269_88e60cb49fa19ed72edeae0db9befde3.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1Eccentric Connectivity Index of Some Dendrimer GraphsM.GHORBANIKH.MALEKJANIA.KHAKIThe eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.EccentricityTopological indexDendrimer graphs20121201718http://ijmc.kashanu.ac.ir/article_5270_22121ef8fc11a8b1d9590fd604033097.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1Computing GA4 Index of Some Graph OperationsM.SAHELIM.JALALI RADThe geometric-arithmetic index is another topological index was defined as 2 deg ( )deg ( ) ( ) deg ( ) deg ( ) G G uv E G G u v GA G u v     , in which degree of vertex u denoted by degG (u). We now define a new version of GA index as 4 ( ) 2 ε ( )ε ( ) ( ) ε ( ) ε ( ) G G e uv E G G G u v GA G   u v    , where εG(u) is the eccentricity of vertex u. In this paper we compute this new topological index for two graph operations.Topological indexGA IndexGA_{4} indexGraph operations201212011928http://ijmc.kashanu.ac.ir/article_5271_e45e1b12bd7d45ac826b874c26ef0661.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1On Symmetry of Some Nano StructuresM.GHORBANIA.ZAEEMBASHIM.SHAHREZAEIA.TABATABAEI ADNANIIt is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. A.T. Balaban introduced some monster graphs and then M. Randic computed complexity indices of them (see A.T. Balaban, Rev. Roum. Chim. 18(1973) 841-853 and M. Randic, Croat. Chem. Acta 74(3)(2001) 683- 705). In this paper, we describe a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs.Weighted graphEuclidean graph201212012936http://ijmc.kashanu.ac.ir/article_5272_4354587496110c6a075b0d1990485b94.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1Applications of Graph OperationsM.TAVAKOLIF.RAHBARNIAIn this paper, some applications of our earlier results in working with chemical graphs are presented.Topological indexGraph operationHierarchical productChemical graph201212013743http://ijmc.kashanu.ac.ir/article_5273_84937ba7dd780549b008d14ef626f331.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1Geometric-Arithmetic Index of Hamiltonian FullerenesH.MOSTAFAEIA.ZAEEMBASHIM.OSTAD RAHIMIA graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.Fullerene graphsHamiltonian graphsGeometric –arithmetic index201212014550http://ijmc.kashanu.ac.ir/article_5274_132874a2fbc48fc20a2cd83418227b21.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1On Counting Polynomials of Some NanostructuresM.GHORBANIM.SONGHORIThe Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.Omega polynomialPI polynomialNanostar dendrimers201212015158http://ijmc.kashanu.ac.ir/article_5275_598bbbb545b1a47f060eba52713bf436.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1Computing Chemical Properties of Molecules by Graphs and Rank PolynomialsM.MOGHARRABG.FATH-TABARThe topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Tutte polynomial of 􀜩 is a polynomial in two variables defined for every undirected graph contains information about connectivity of the graph. The Padmakar-Ivan, vertex Padmakar-Ivan polynomials of a graph 􀜩 are polynomials in one variable defined for every simple connected graphs that are undirected. In this paper, we compute these polynomials of two infinite classes of dendrimer nanostars.DendrimersTutte polynomialPI-polynomial201212015965http://ijmc.kashanu.ac.ir/article_5276_79a271992b7bcfde9d597fe6eba83405.pdf2012-12-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920123Supplement 1A Note on Atom Bond Connectivity IndexS.HEIDARI RADA.KHAKIThe atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.Topological indexABC IndexNanotubeNanotori201212016775http://ijmc.kashanu.ac.ir/article_5277_d209553fa79f35c61cae445c78d6baa4.pdf